Question: Rewrite as a simplified fraction. ${3.5\overline{67} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3567.6767...\\ 10x &= 35.6767...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3532}$ ${x = \dfrac{3532}{990}} $ ${x = \dfrac{1766}{495}} \text{or} {3 \dfrac{281}{495}}$